For centuries, scientists have attempted to identify and documentanalytical laws that underlie physical phenomena in nature.Despite the prevalence of computing power, the process of findingnatural laws and their corresponding equations has resistedautomation. A key challenge to finding analytic relations automaticallyis defining algorithmically what makes a correlation in observeddata important and insightful. We propose a principle for theidentification of nontriviality. We demonstrated this approachby automatically searching motion-tracking data captured fromvarious physical systems, ranging from simple harmonic oscillatorsto chaotic double-pendula. Without any prior knowledge aboutphysics, kinematics, or geometry, the algorithm discovered Hamiltonians,Lagrangians, and other laws of geometric and momentum conservation.The discovery rate accelerated as laws found for simpler systemswere used to bootstrap explanations for more complex systems,gradually uncovering the “alphabet” used to describe those systems.